I want to perform a chi-square test for a 2x2 table. Given that I might expect p-value < 0.05, how can I estimate the required sample size?


In order to estimate your sample, you need to know

  • which statistical significance (type I error) you want to reach
  • what statistical power (1 - type II error) you want to reach
  • which minimal detectable difference you want to see in your data

One of the most used methods to estimate your sample size is given in the book "Statistical Methods for Rates and Proportions" of Fleiss (1973). See page 72, equation 4.15 for the corrected formula.

Here is the equation:

enter image description here

  • $n'$ is sample size without continuity correction
  • $n$ is sample size with the correction
  • $P_1$, $P_2$, are proportions in each group
  • $Q_1 = 1 - P_1$
  • $\bar P = \frac{P_1 + P_2}{2}$
  • $z_{\alpha/2}$ is value cutting off the proportion $\alpha / 2$ in the upper tail of the standard normal curve. (same for $z_\beta$)

You can find an implementation of it in R: power.prop.test in the stats package.

| cite | improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.